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16
Shuffling cards and stopping times
 In Proceedings of the 43rd IEEE Conference on Decision and Control
, 1986
"... 1. Introduction. How many times must a deck of cards be shuffled until it is close to random? There is an elementary technique which often yields sharp estimates in such problems. The method is best understood through a simple example. EXAMPLE1. Top in at random shuffle. Consider the following metho ..."
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Cited by 93 (11 self)
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1. Introduction. How many times must a deck of cards be shuffled until it is close to random? There is an elementary technique which often yields sharp estimates in such problems. The method is best understood through a simple example. EXAMPLE1. Top in at random shuffle. Consider the following method of mixing a deck of cards: the top card is removed and inserted into the deck at a random position. This procedure is
Rates of Convergence for Gibbs Sampling for Variance Component Models
 Ann. Stat
, 1991
"... This paper analyzes the Gibbs sampler applied to a standard variance component model, and considers the question of how many iterations are required for convergence. It is proved that for K location parameters, with J observations each, the number of iterations required for convergence (for large K ..."
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Cited by 38 (10 self)
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This paper analyzes the Gibbs sampler applied to a standard variance component model, and considers the question of how many iterations are required for convergence. It is proved that for K location parameters, with J observations each, the number of iterations required for convergence (for large K and J) is a constant times
Rates of Convergence for Data Augmentation on Finite Sample Spaces
 Ann. Appl. Prob
, 1993
"... this paper, we examine this rate of convergence more carefully. We restrict our attention to the case where ..."
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Cited by 24 (13 self)
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this paper, we examine this rate of convergence more carefully. We restrict our attention to the case where
Onedimensional linear recursions with Markovdependent coefficients
, 2004
"... For a class of stationary Markovdependent sequences (ξn,ρn) ∈ R 2, we consider the random linear recursion Sn = ξn + ρnSn−1, n ∈ Z, and show that the distribution tail of its stationary solution has a power law decay. An application to random walks in random environments is discussed. MSC2000: pri ..."
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Cited by 7 (0 self)
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For a class of stationary Markovdependent sequences (ξn,ρn) ∈ R 2, we consider the random linear recursion Sn = ξn + ρnSn−1, n ∈ Z, and show that the distribution tail of its stationary solution has a power law decay. An application to random walks in random environments is discussed. MSC2000: primary 60K15; secondary 60K20, 60K37.
RENEWAL THEORY FOR FUNCTIONALS OF A MARKOV CHAIN WITH COMPACT STATE SPACE
, 2003
"... Motivated by multivariate random recurrence equations we prove a new analogue of the Key Renewal Theorem for functionals of a Markov chain with compact state space in the spirit of Kesten [Ann. Probab. 2 (1974) 355–386]. Compactness of the state space and a certain continuity condition allows us to ..."
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Cited by 6 (4 self)
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Motivated by multivariate random recurrence equations we prove a new analogue of the Key Renewal Theorem for functionals of a Markov chain with compact state space in the spirit of Kesten [Ann. Probab. 2 (1974) 355–386]. Compactness of the state space and a certain continuity condition allows us to simplify Kesten’s proof considerably.
RENEWAL THEORY IN ANALYSIS OF TRIES AND STRINGS
"... To my colleague and friend Allan Gut on the occasion of his retirement Abstract. We give a survey of a number of simple applications of renewal theory to problems on random strings and tries: insertion depth, size, insertion mode and imbalance of tries; variations for btries and Patricia tries; Kho ..."
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Cited by 1 (1 self)
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To my colleague and friend Allan Gut on the occasion of his retirement Abstract. We give a survey of a number of simple applications of renewal theory to problems on random strings and tries: insertion depth, size, insertion mode and imbalance of tries; variations for btries and Patricia tries; Khodak and Tunstall codes. 1.
Markov Additive Processes and Reflecting Brownian Motion in a Cone
"... After applying a certain space and time transformation, a (semimartingale) reflecting Brownian motion without drift in a cone, whose reflection directions are radially homogeneous, becomes a Markov additive process. This observation is a simple manifestation of the invariance of such processes unde ..."
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After applying a certain space and time transformation, a (semimartingale) reflecting Brownian motion without drift in a cone, whose reflection directions are radially homogeneous, becomes a Markov additive process. This observation is a simple manifestation of the invariance of such processes under a scaling. Markov additive processes are familiar in queueing theory, especially in Matrix Analytic Methods. The answers to some important questions about reflecting Brownian motion may be guessed by analogy with wellknown results in Matrix Analytic Methods.
Springer For Sylviane, Melanie and DanielPreface
, 2010
"... Use the template preface.tex together with the Springer document class SVMono (monographtype books) or SVMult (edited books) to style your preface in the Springer layout. A preface is a book’s preliminary statement, usually written by the author or editor of a work, which states its origin, scope, ..."
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Use the template preface.tex together with the Springer document class SVMono (monographtype books) or SVMult (edited books) to style your preface in the Springer layout. A preface is a book’s preliminary statement, usually written by the author or editor of a work, which states its origin, scope, purpose, plan, and intended audience, and which sometimes includes afterthoughts and acknowledgments of assistance. When written by a person other than the author, it is called a foreword. The preface or foreword is distinct from the introduction, which deals with the subject of the work. Customarily acknowledgments are included as last part of the preface. Place(s), month year
The Key Renewal Theorem for a Transient Markov Chain
, 711
"... We consider a timehomogeneous Markov chain Xn, n ≥ 0, valued in R. Suppose that this chain is transient, that is, Xn generates a σfinite renewal measure. We prove the key renewal theorem under condition that this chain has asymptotically homogeneous at infinity jumps and asymptotically positive dr ..."
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We consider a timehomogeneous Markov chain Xn, n ≥ 0, valued in R. Suppose that this chain is transient, that is, Xn generates a σfinite renewal measure. We prove the key renewal theorem under condition that this chain has asymptotically homogeneous at infinity jumps and asymptotically positive drift.